Adaptive Sliding Mode Control for Spacecraft Proximity Operations Based on Dual Quaternions

摘要

This paper proposes an adaptive sliding mode control law based on dual quaternions for six-degree-of-freedom proximity operations between a chaser and a target spacecraft. Dual quaternion, a new parameterization to simultaneously describe the translation and the rotation of a rigid body, is used to model the relative motions during proximity operations. The novelty of the proposed sliding mode controller is that, by exploring the similarity between dual quaternions and quaternions, the sliding surface is designed based on basic dual quaternion algebra without introducing the logarithm of dual quaternions. The unwinding phenomenon is taken into consideration in the design of the sliding surface. The uncertainties in the mass property (i.e., the mass and the inertia matrix) of the chaser and external disturbance forces and torques (bounded but unknown) exerted on the chaser are considered. The closed-loop stability of the relative translational and relative rotational motions is proven using the Lyapunov method. The chattering effect of the sliding mode control is alleviated by replacing the sign function with the sigmoid function. With this modification, the sliding variable can only converge to a neighborhood of the ideal sliding mode. Simulation results are provided to demonstrate the performance of the proposed controller.